June 5 , 1961
2415
PREFERENTIAL HYDRATION OF PROTEIKS
In the case of bovine serum albumin, this possibility is lively indeed. Sharp single bands were, however, obtained with myosin, H-meromyosin and lysozyme. Multiple bands were observed with all of the other proteins studied, but in each o f these latter cases, excepting only that of BSA,
there was reason to doubt the homogeneity of the protein sample. The question as to how commonly a single protein species will give more than one band of precipitate requires further study, but the method deserves closer examination as a criterion of the homogeneity of protein samples.
[CONTRIBUTIOS FROX THE BIOCHEMISTRY DEPARTMENT, SCHOOL OF MEDICINE, UNIVERSITY OF PENSSYLVANIA, PHILADELPHIA, P A . ]
The Preferential Hydration of Proteins in Concentrated Salt Solutions. 111. Theoreticall BY VERNEN. SCHUMAKER AND DAVID J. Cox RECEIVED NOVEMBER 19, 1960 Equations are developed showing the relation between the binding of ions by macromolecules and preferential hydration. I t is suggested t h a t the hydration of the salt ions in solution is the primary factor responsible for the preferential hydration of the macromolecule.
Equations governing the interaction between ions and macromolecules have been developed by a number of investigators.3 These binding equations are based upon the mass law and treat the macromolecule as possessing a number of specific ion binding sites having definite association constants for interaction with the small ions. Equations have been developed by other workers who have studied the phenomenon of preferential hydration of macromolecules. The macromolecule is considered by these workers to interact with a number of water molecules and a smaller number of ions. If the proportion of water molecules to salt ions in the vicinity of the macromolecule is greater than the proportion of water to salt in the solvent, the preferential hydration is positive. If salt is in excess, the preferential hydration is negative. Interestingly, investigators studying ion binding often find that proteins bind sizable numbers of salt ions in solution. Other investigators studying preferential hydration find that proteins bind large quantities of water to the exclusion of salt. In this communication we have joined together the ion binding equations and the preferential hydration equations. As might be expected, the resulting expression clearly shows that a t low concentrations of salt ions, the macromolecules preferentially bind salt while a t high concentrations of salt, the macromolecules preferentially bind water. Indeed, it becomes clear that ion binding and preferential hydration are, experimentally, difficult to separate. One result of this treatment is to suggest that the interpretation of ion binding results, such as determined in the e.m.f. cell or by equilibrium dialysis, (1) This investigation was supported by Research Grant 8 - 2 1 7 7 from t h e Xational Institute of Arthritis and Metabolic Diseases of t h e National Institutes of Health, United States Public Health Service, IS. S. A. One of us (D.J.C.) was a pre-doctorate fellow of t h e National Science Foundation, 1956-1959. (2) Reviewed by I. hl. Klotz, in "Proteins," Vol. I , P a r t B, H. S e u r a t h and K. Bailey, Editors, Academic Press, Inc., New York, N. Y., 1953, p , 763. (3) S. Katz and H . K. Schachman, Biochcm. e l . Biofihys. A d a , 81, 28 (1955).
may contain small but definite errors if a correction for preferential hydration is not made. In addition, we present in this communication a reasonable physical mechanism for preferential hydration of macromolecules in salt solutions. In this mechanism, attention is directed to the ionized salt which interacts strongly with adjacent water molecules through ion-dipole bonds. As the salt ion is brought to the surface of the macromolecule, electrostatic allegiances shift, new bonds may arise and water molecules may be freed. Should these events be energetically unfavorable, the ion concentration will drop sharply in the surface layer. Effectively, the macromolecule will be preferentially hydrated even though there is little or no positive interaction between it and the water.
Theory In this section it is shown that preferential hydration may be expressed mathematically in terms of ion binding by considering all the binding energies, positive and negative, over the entire surface of the macromolecule. The surface layers surrounding the macromolecule will be defined as the monolayer of solvent in contact with atoms of the macromolecule together with several adjacent layers of solvent. For ease of mathematical formulation the sizes of. the water molecules and the unhydrated salt ions are considered t o be equal so that the surface layers will contain X water molecules and salt ions regardless of the composition of the layers. I n general the surface of the large molecule will be inhomogeneous in binding affinities for the salt ions, and i t can be divided into groups of sites i, each group containing X i members possessing an intrinsic affinity constant kij for a particular ion, j . For interaction between small molecules and a macromolecule, the mass law may be conveniently written2 yij
Xikijm, = ___-
+
(1) 1 kijmj where rij is equal to the number of moles of salt ions of species j bound a t sites of type i, mj is the molality of the free (unbound) ion, and k i i is the intrinsic association constant for this reaction. Kow, if the composition of solvent bound a t the X i sites is t o be the same as the composition of the free solvent, then there would have to be r i j (55.51/mj) water molecules bound a t the sites, X i . The difference between this number and the number of water molecules actually bound, ( X i - r , j ) will be termed the preferential hydration, aii cy"' J
-
(Xi
-
Ti;)
- rij 55.51 mi
VERXE X. SCNUMAKER AND DAVID J. Cox
2446
T h e preferential hydration, a i j , is equal t o the number of water molecules at t h e sites i in excess or dearth of the number needed to “balance” the bound ions of species j . It may be either positive or negative, and if i t is negative the macromolecule is considered t o be binding ions preferentially at the sites i. The rij may be eliminated between equatioris 1 and 2 gi vi I 1g4
(3) The a i j can finally be summed over the groups of sites i t o give aj =
cvij
(4)
j
This quantity, aj, is the preferential hydration of the entire macromolecule with respect to ion species j . A similar equation can be written for ions of the opposite charge and will in general, give a different value for aj. Ion Binding Studies.-It will now be shown t h a t in some types of ion binding studies the quantity actually nieasurcd is the preferential hydration, aj,with respect to a particular ion species as defined by equation 4 . I n these studies the molality of a free ion, mj, is measured in a solution containing E kilograms of water, njo moles of ion j , and np moles of proteiii. The usual procedure is then to calculate a number, I’&d., by the type of equation5 nprobsd = ??io - mjg (5) On the other hand, the experiniental results may be in-
terpreted more properly in terms of the preferential hydration, aj. Upon addition of n p moles of macromolecule, let rjn, be the number of moles of salt ions t h a t are actually bound. Then ( h - rj)n,, moles of water which d o not contain salt ions of species i are present a t the remainder of the sites. The complete expression lor v t j is therefore giveu
which can be rearranged to give
56.51 B u t according to equation 5 , the left hand side of equation 7 is equal to n p i & , s d . Moreover, the expression in brackets on the right hand side of equation 7 is equal t o a,.. This is directly seen by summing equdtion 2 over the sites I . Thus, equation 7 becomes
Therefore, the r o b & is simply related t o the preferential hydration a l . This is an important result, for equations 3 and 4 show t h a t aj may be composed of several groups of sites inrlitding thoae which exclude ions strongly. L e t us coiisider a simple case of a macromolecule possessing A, sites a t which ions are completely excluded, and hb sites a t yhicli they are bound firmly with a n intrinsic association colistant KO. Then equatioiis 3 arid 4 give ( 1 --- kO -5 5 . 5 1 ) cy, = A, Ah (9) (1 komj) Sliould A, be large and Ab small, appreciable errors can result if r,~,~d arid aj are interpreted in terms of hb only. For example, if A, = 1000, hb = I O , and kO = 59, the calculated binding will l~ apprs.tirnately 55% too low when the salt concentration is 0.01 N , and approximately 2070 too low at a Concentration of 0.1 JI. Even a t infinite dilution appreciable errors may occur :IS may be seen in equation 9 by letting m j approach zero. A better value can
+
+
(4) I n concentrated salt solutions individu:il ion activity coefficients should be used in equation 3. I n lieu of having these, but less correctly, t h e mean ioil activity coefficients may be used. In equation 3 t h e activity coefficient for t h e salt iou will appear a s a coefficient of k:..O in ’ equations 1 and 3 a s suggested by C. Tanford and J. G. Kirkwood, J . A m . Chem. Suc., 79, 5333 ( 1 9 3 i ) . or a s suggested in ref. 5. ( 5 ) G. Scatchard, I. H. Schcinberg and S. €I. Armstrong, Jr., J . Aiu. C h e m . Soc., 72, 535 (10.50).
,,
1701.83
be obtained if he is first dettmiiined from Iirefrrcnlial Iiydra1 ion studies made at very high salt coticentr:itions whcre tlie secuiid term on the right in equation 7 k!C(JliieS small iri comparison with A,. 111 Fig. 1 is shon-n :I piot r)f equatioii 9 for a h).p(ithelical protei11 with A, = IOiJij, AI, = 10 aiid kO = 50. Equilibrium Dialysis Studies.---Katz 113s pointed out t h a t the qu;!:itity :ictually measured iii eqiii1ii)riuin dialysis experiments is the specific adsorption ccieficient which is defined thermodynamically :ind may I J interpreted ~ iii terms of the preferential hytlratioii i u simple three conipoilent systems such as water, sucrose and protein.* -4 inore complicated trtAa1iiient is necessary for t h e development of equations which consider prefcreritinl hydration iri equilibrium dialT-sis s!udies of ion binding to macromolecules. The develcpment will not be presented here, but tlie final expression for a solution containing isoionic proteiii and a uni-univaleiit electrolyte is
where a+ and 01- are the preferential hydratiori values tor the cation and aiiion, g is the number of kilograms of water inside the dialysis sac, n p is the number of moles of the macromolecule, n is the total number of nioles of salt (or of either ion) inside the sac antl in’ is the molality of salt outside the sac. Ii-hile this equation is readily derived in a rigorous fashion, its validity can be seen upon close inspection. The terms in brackets on the left represent the effective quantities of water in which all the cations or anions, including those bound to the macromalecule, would have t o be dissolvetl to give the molalities rn+ and m , which are the actual molalities of the free (unbound) ions inside the sac. The ( m ’ ) P = na+na-, RS the condition of equilibrium. When each of these molalities, m+ and nt-, is multiplied by the effective quantity of water, the result is equal t o the total number of moles of anion or cation inside the sac, n. Sedimentation Sttldies.--Xs can be seen from a n inspection of equation 4, rhe value of aj becomes more positive as inj increases. Therefore by measuring aj over a witlix range of concentrations it may become possible to estimate both the number of sites of exclusioti and of binding. Ultracentrifugation may offer a n approach t o the problem of measuring a in high salt concentrations. If ultracentrifugation is t o be used, however, two related problems immediately arise. Equation 4 can be written for both thy anion :rid for the c:ition, and in general a+ and a- will bc different. But the ultr3ceritrifiigation studies give but one value for C Y , and it is not obvious to us how this N is related to a+ and a- . Secondly, if at and 01- are different, the number of bound anions and cations are different, antl the sedimentiiig unit carries a net charge. I n this caw, charge efiects. especially the secondary charge effect, could affect the sedimentation properties of the hydrodynaniic unit. For bovine serum albumin, a voracious ion binder, these difficulties may explain the wide variety of results obtainetl for a by ultracentrifugation iu different solvents and a t different pFI values. For ribonuclease, on the other hand, the experimen::.l value for a remained unchanged in a number of salt soliltioiis and over a wide range of Concentrations. It also was iiidependcnt of PH. I t appears reasonable t o assume tl::i t for this protein, a+ aud 01- are similar or identical, antl t h i . the net charge carried b y this protein is small. In thi. c;ise the centrifugation studies should give 01j. Therefore, if values for a,are to bc measured by centrifrication studies, n-e feel tliat me:wirements should be mo(’(. ovcr a range of salt conrelitrations and in a variety solvents. If under these conditions the calculated (Y remains constant, it appears reasoriahle to assume that i t is :I \?ah1 nic~asiire of preferential hydrotion.
Discussion mnts of water are associated with r i h i i u c l e a s e an:? Imvixe serum albumin in roncentra tctl salt solutions as shown in our previous studies.’ ( 6 ) S. Ratz, ibid., 7 8 , 300 (195fj). (7) n. J. Cox and V. h‘, Schumaker, i b i d . , 8 3 , 3433, ?43’l ( 1S l i l \ .
Juiie 5 , 1961
PKEPERENTIAL HYDRATION O F
It may be asked if a monolayer of water over the surface of these proteins would account for the large hydration values obtained. The minimum surface areas for these proteins which may be ~$1culated from spheresoof equal volume are 3000 A.2 for RNase and 9000 A.2for BSA. From the molecular weight and density of water we limy assign a 3.1 A. cube to each water molecule. Therefore, a monolayer of water around the equivalent sphere would correspond to a preferential hydration value of 0.4 g. HrO ’g protein for RNase. For BSX the corresponding value would be 0 25 g. H 2 0 / g . protein. These values are certainly the same magnitude as the observed results; surface irregularities and deviation from spherical shape will tend to make the approximate calculations too small. In order to apply this theory to proteins, it is necessary to consider the interaction between salt ions and the several grmps of sites which exist a t the surfaces of these macromolecules. From equations 3 and 4 it can be seen that for the preferential hydration to be positive a t all, a t least one of the terms K , , j o (55.51) must be less than unity. This means that the standard free energy of ion binding must be positive: AFo = -RT In (1’5551) = +2339 cal. a t 20’. In solution the salt ions are symmetrically hydrated with water molecules held in place by strong ion-dipole forces. In order for the salt ion to participate In the monolayer adjacent to the macromolecule, this hydration shell must be distorted. It is difficult to estimate the energies that would be involved in this distortion, but it is reasonable to expect that they are positive and quite large. We suggest that this is the primary factor involved in the preferential hydration of proteins in concentrated salt solutions. For the hydrophobic side chains (valine, phenylalanine, etc.,) the values of k” (55.51) are probably very small indeed. A shell of water might be expected to form within such hydrophobic regions. This view is, perhaps, essentially different from the suggestion of K l o t ~ that * ~ ~the hydrophobic side chains cause an ordering of neighboring water molecules, but the end result might be much the same. Such a shell would tend to exclude the hydrated hydronium ion, thereby changing pK values of acidic and basic groups buried in such regions. For those sites a t the surface of the protein formed by peptide bonds and uncharged nitrogen and oxygen atoms, two additional factors must be considered. The free energy would be expected to be somewhat lower than that found for the hydrophobic regions because of the stronger induced dipole that would be created in such regions upon the approach of the ion. On the other hand, hydrogen bonds are thought to exist between water and many of the nitrogen and oxygen atoms on the surface of the protein. The presence of such bonds might contribute fl or +2 kcal. to AFO, particularly a t sites adjacent to peptide bonds. Considering then these two additional factors the preferential hydration probably still is positive, but it may not be complete. Next, i t is necessary to consider the sites of charged acidic and basic groups. Ions (8) I. M. Klotz, Science, 1’28,R15 (10iS). (9) I. M Klotz, in ‘Syinposlurn on Silt and Water XIetiholism,” C i r r u l n t t o n 2 1 , 828 ( 1 w T
PROTEINS
2447
Fig. 1.-Preferential hydration values, aj, for a hypothetical protein possessii~g 1000 sites from which ions of species j are completely excluded, m d 10 ion binding sites for which the intrinsic association constant, ko, is 50. Tlte curYe is deteririined by equation 9.
of the same charge would be strongly repelled, and with respect to these ions the hydration would be large a t such sites. For ions of opposite charge the binding affinities a t charged sites are probably greatest and the values of o,j small or even negative. The actual values will depend upon the type of ion, type of site, steric factors and the neighboring charge distribution. However, large quantities of Na+, I(+ and C1-, usually do not bind copiously to isoelectric proteins2 which contain many such charged acidic and basic groups. Therefore, a number of factors must combine to make a specific ion binding site. lo In conclusion, it may be pointed out that it is possible to explain hydration without invoking any forces except those of steric exclusion. Hydration would occur if the macromolecules were selectively permeable to water through channels which could admit water molecules but because of their small size would exclude larger solutes. The small hole through the center of the hemoglobin moleculc discovered by Perutz and co-workers” may be such a channel. Kauzmann (cited by Schachman and Lauffer12) has suggested another explanation which does not involve attractive forces as the primary factor. If the density increasing com(10) Uncharged imidazole residues have been implicated in the binding of the zinc ion to serum albumin. Therefore, charged groups may not be essential for the binding of ions at certain speci6c sites where they might form coordinate linkages. (11) M. F. Perutz, M. G. Rossmann, A. P. Cullis, H. Muirhead, G . Will and A . C. T. North, Nature, 185, 418 (1960). (12) H. K. Schachman and M. A. Lauffer, J . A m . Chem. SOL.,71,
536 (1949).
ponent (urea, sucrose, etc.,) is larger than the water molecules and considered to be composed of "rigid, uncharged spheres of radius, a, it is clear that the center of any of these molecules will not he able to come closer than a distance, a, t o the 'surface' of the sedimenting particle. This results in a region of thickness, Za, surrounding the macromolecules in which the density varies from that of water to that of the solution. According to Kauzmann, this region of varying density can be approximated by assigning a water layer of thick-
[CONTRIBUTION FROM
THE
ness, a, to the macromolecules and assuming that the liquid more distant than a, from the surface of the macromolecule has the density of the bulk l i q ~ i d . ' ~ "In such cases as these, it is still possible to use the equations developed in the theoretical section of this communication. The 01) will r e f e l to the number of water molecules in the region from which salt is excluded, and the binding afFinities. k', for such regions will be equal to zero. (13) W . IC. Schachman, "Ultracentrifugation in 13iwliemi\try:" Academic Press, Inc , S e w York, N . Y . , 105'3, p. X R .
DEPARTMENT O F CHEMISTRY, CORNELL UNIVERSITY,
ITHACA, KE\V
YORK]
A Raman Study of the Bromide Solutions of Zinc and Cadmium'" BY WILBURYELL IN'^
AND
ROBERTA. PLANE
RECEIVEDNOVEMBER 14, 1960 Raman intensity measurements were made of zinc bromide solutions containing various ratios of total zinc t o total broinide. These results led t o the following as the most probable assignments for the three polarized lines: V I , ? cm. ( p = 0.06), ZnBrc'; Y I S B crn.-' ( p = 0.09), ZnBr?; uZoj cm.-l ( p = 0.13), ZnBr ?. Comparison with ZnBrp in nun-aqueous solvents indicated t h a t t h e aqueous ZnBra molecule is different from t h a t in other solvents and may be tetrahedral Zti(HnO)?Brr. Stepwise formation constants for the three complexes were found in concentrated solution t o be: (ZnBr +) /i%n+ + ) ( B r - ) = 0.3, (ZnBr2)!(ZnBr+)(Br-) = 1, (ZnBrl')!(ZnBr*)(Br-)a = 0.2. If ZnBra- were present, its principal Kainan band \vas coincident with t h a t of one of the other species. I n cadmium bromide solution of various ratios of total B r - t o total C d only one polarized line was found. Coincident with t h a t line, a t 166 cm.-l ( p = 0.08) which was due t o CdBrc-, was the principal line of one (or more) lower species. The lower species appeared t o be of less importance than in the zinc systein, while the tetrabromo species was of greater importance: (CdBrc=),'(Cd'+)(Br-)4> 1. ?,
Of the methods used for studying complex ions Aqueous solutions of Znti- and Br- had been in aqueous solution, none is more direct than the found to show Raman lines a t 172, 1S-l and 20s measurement of Raman spectra of solutions. This c m - I , while non-aqueous solutions of ZnBr2 method is direct in that each different complex showed a line a t (or near) 208 cm. and in some species present should exhibit its characteristic solvents a second line a t 172 ern.-'. On this vibrational spectrum.2 Thus, the Raman method basis, the line a t 208 em.-' was assigned to the differs from most other methods which determine linear ZnBrY molecule, that a t 172 cm.-' to the some property characteristics of one species (often tetrahedral ZnBrr= (whose other frequencies were the activity of the completely dissociated species) found to be 61, 82 and 210 cm.-lj and the interand from variations of this property infer the mediate line (184 cm. -') found only in water was presence of additional species. Furthermore, the assigned to ZnBr3--. No Raman evidence was very existence of a Raman spectrum shows that the found for any other species such as ZnBr+, for complex species has kinetic identity (ie., exists for which non-Raman evidence Previous times long enough to allow vibrations) and is bound studies of aqueous cadmium bromide solutions together by something other than hard-sphere detected the existence of only the tetrahedral coulombic attractions (;,e., the mean molecular CdBr4'.5 Thus, a primary aim of the present polarizability must change during vibration3). investigation was to determine which lower comThus, in principle, observation of Raman spectra is plexes are formed in aqueous solutions of the a general method for both defining and detecting bromides of zinc and cadmium. Quantitative illcomplex ions in aqueous solutions. tensity measurements were made both for this The present work was undertaken in order to purpose and t o determine the concentrations of the study as quantitatively as possibly Raman spectra various species as a function of solution composiof concentrated aqueous solutions containing rela- tion. tively simple complex ions. For the investigation, Experimental the bromides of zinc and cadmium were chosen. Measurements were made with a Cary Model 81 Ranian Both had previously been studied q ~ a l i t a t i v e l y . ~spectrophotometer. ~~ This instrument was altered 0 1 1 1 ~i i i (1) (a) This work was supported by t h e United States ilir Force through t h e Air Force Office of Scientific Research of t h e Air Research and Development Command, under Contract N o . A F 49(635)279. Reproduction in whole or in p a r t is permitted for any purpose of t h e United States Government. Some of t h e results were reported a t t h e 136th National Meeting of t h e American Chemical Society, .4tlantic City, New Jersey, September, 1959. (b) Based on work performed for partial fulfillment of t h e degree of Doctor of Philosophy. 12) G. W. Chantry and R. A. Plane, J . Chem. Phys., 33, 736 (1960). (3) Cf. D . A . Long, Proc. Roy. Sac. (London), B a l l , 203 (1963). I. -4. \%'oorlward and D. A. I,ong, Trans. F a r a d a y SOC.,45, 1131 i lW9).
t h a t the filter solution was replaced by pure isopropyl alcohol and sample tubes were used which were specially (4) M , L. Delwaulle, Conipl. v e n d . , 240, 2132 (1%5);
B d . Soc.
Chim.,France, 1966, 1294 (1955). (3) J. A. Rolfe, D. E. Sheppard and I.. A . Woodward, Trans. F a r a d a y Soc., 50, 1275 (1954).
(6) E. Ferrell, J. 51. Ridgion and H. I,. Riley, J . Chduz. .Soc., 1121 (193G). (7) (a) L. G. Sillen and B . Tiljequist, S v e n s k k e w . T i d s k r . , 56, 8: (1944); (b) S. A. Shchukarev, I.. S . 1,ilich a n d V. A . Latysheva, Z / I I O , . i i m v g . K h i w . , 1, 2 2 3 (19,X),
